EASy Summer 2006Non Symbolic AI Lecture 131 Non Symbolic AI - Lecture 13 Symbolic AI is often associated with the idea that “ Intelligence is Computation” and “The Brain is a Computer” Non Symbolic AI is often associated with the idea that “Intelligence is Adaptive Behaviour” and “it arises from the dynamical interactions of networks of simple components” Eg ANNs (Artificial Neural Networks)

EASy Summer 2006Non Symbolic AI Lecture 132 Cellular Automata (and Random Boolean Networks) These are another class of systems that fit this last description. In the wide spectrum of approaches to synthesising 'lifelike' behaviour, CA s and RBN s are amongst the most abstract and mathematical. A lot of the interest in this comes from people with a Physics background. Cf. Los Alamos, Santa Fe, the 'chaos cabal'. (pop book on the chaos cabal: "The Newtonian Casino” T. Bass 1990 Longmans, (US= "The Eudaemonic Pie" 1985)

EASy Summer 2006Non Symbolic AI Lecture 133 The Game of Life Best known CA is John Horton Conway's "Game of Life". Invented 1970 in Cambridge. Objective: To make a 'game' as unpredictable as possible with the simplest possible rules. 2-dimensional grid of squares on a (possibly infinite) plane. Each square can be blank (white) or occupied (black).

EASy Summer 2006Non Symbolic AI Lecture 134 More Game of Life At any time there are a number of squares with black dots. At the 'regular tick of a clock' all squares are updated simultaneously, according to a few simple rules, depending on the local situation. For the 'Game of Life' local situation means, for any one cell, the current values of itself and 8 immediate neighbours ('Moore neighbourhood')

EASy Summer 2006Non Symbolic AI Lecture 135 NeighbourhoodsNeighbourhoods 8 immediate neighbours = 'Moore neighbourhood’, on L For different CAs, different neighbourhoods might be chosen; e.g. the 'von Neumann neighbourhood', on R. Readable pop sci on CAs: William Poundstone "The Recursive Universe" OUP 1985

EASy Summer 2006Non Symbolic AI Lecture 136 Game of Life: rules Update rule for each cell: If you have exactly 2 'on' nbrs (ie 2 blacks) stay the same If you have exactly 3 'on' nbrs you will be 'on' (black) next timestep (ie change to on if you are blank, and remain on if you already are) If you have less than 2, or more than 3 on nbrs you will be off (blank) next timestep Thats all !

EASy Summer 2006Non Symbolic AI Lecture 137 GliderGlider

EASy Summer 2006Non Symbolic AI Lecture 138 SequencesSequences

EASy Summer 2006Non Symbolic AI Lecture 139 MoreMore Sequence leading to Blinkers Clock Barber’s pole

EASy Summer 2006Non Symbolic AI Lecture 1310 A Glider Gun

EASy Summer 2006Non Symbolic AI Lecture 1311 More formal definition of CA A regular lattice eg. grid of finite automata eg. cells each of which can be in one eg. black/white tho of a finite number of states could be 10 or 100 transitions between states are governed by a state-transition table eg. GoL rules input to rule-table = state of cell and specified local neighbourhood (In GoL 2 ^9 = 512 inputs) output of rule-table = next state of that cell

EASy Summer 2006Non Symbolic AI Lecture 1312 CAsCAs All automata in the lattice (all cells on the grid) obey the same transition table, and are updated simultaneously. From any starting setup on the lattice, at each timestep everything changes deterministically according to the rule- table.

EASy Summer 2006Non Symbolic AI Lecture 1313 Game of Life: rules (again!) Update rule for each cell: If you have exactly 2 'on' nbrs (ie 2 blacks) stay the same If you have exactly 3 'on' nbrs you will be 'on' (black) next timestep (ie change to on if you are blank, and remain on if you already are) If you have less than 2, or more than 3 on nbrs you will be off (blank) next timestep Thats all !

EASy Summer 2006Non Symbolic AI Lecture 1314 Alternative version of rules Every cell is updated simultaneously, according to these rules, at each timestep. Alternative (equivalent) formulation of Game of Life rules: 0,1 nbrs = starve, die 2 nbrs = stay alive 3 nbrs = new birth 4+ nbrs = stifle, die

EASy Summer 2006Non Symbolic AI Lecture 1315 Gliders and pentominoes On the left: a 'Glider' On a clear background, this shape will 'move' to the NorthEast one cell diagonally after 4 timesteps. Each cell does not 'move', but the 'pattern of cells‘ can be seen by an observer as a glider travelling across the background.

EASy Summer 2006Non Symbolic AI Lecture 1316 EmergenceEmergence This behaviour can be observed as ‘the movement of a glider’, even though no glider was mentioned in the rules. 'Emergent' behaviour at a higher level of description, emerging from simple low-level rules. Emergence = emergence-in-the-eye-of-the-beholder (dangerous word, controversial)

EASy Summer 2006Non Symbolic AI Lecture 1317 PentominoesPentominoes On the right: a 'pentomino'. Simple starting state on a blank background => immense complexity, over 1000 steps before it settles. (Pop Sci) William Poundstone "The Recursive Universe" OUP 1985 (Primordial Soup kitchen)

EASy Summer 2006Non Symbolic AI Lecture 1318 Game of Life - implications Typical Artificial Life, or Non-Symbolic AI, computational paradigm: bottom-up parallel locally-determined Complex behaviour from (... emergent from...) simple rules. Gliders, blocks, traffic lights, blinkers, glider-guns, eaters, puffer-trains...

EASy Summer 2006Non Symbolic AI Lecture 1319 Game of Life as a Computer ? Higher-level units in GoL can in principle be assembled into complex 'machines' -- even into a full computer, or Universal Turing Machine. (Berlekamp, Conway and Guy, "Winning Ways" vol 2, Academic Press New York 1982) 'Computer memory' held as 'bits' denoted by 'blocks‘ laid out in a row stretching out as a potentially infinite 'tape'. Bits can be turned on/off by well-aimed gliders.

EASy Summer 2006Non Symbolic AI Lecture 1320 Self-reproducing CAs von Neumann saw CAs as a good framework for studying the necessary and sufficient conditions for self-replication of structures. von N's approach: self-rep of abstract structures, in the sense that gliders are abstract structures. His CA had 29 possible states for each cell (compare with Game of Life 2, black and white) and his minimum self-rep structure had some 200,000 cells. // PAUSE --- END – is OK !! --Dustin.

EASy Summer 2006Non Symbolic AI Lecture 1321 Self-rep and DNA This was early 1950s, pre-discovery of DNA, but von N's machine had clear analogue of DNA which is both: used to determine pattern of 'body' interpreted and itself copied directly copied without interpretation as a symbol string Simplest general logical form of reproduction (?) How simple can you get?

EASy Summer 2006Non Symbolic AI Lecture 1322 Langton’s Loops Chris Langton formulated a much simpler form of self-rep structure - Langton's loops - with only a few different states, and only small starting structures.

EASy Summer 2006Non Symbolic AI Lecture 1323 SnowflakesSnowflakes

EASy Summer 2006Non Symbolic AI Lecture 1324 One dimensional CAs Game of Life is 2-D. Many simpler 1-D CAs have been studied, indeed whole classes of CAs have been. Eg. a 1-D CA with 5 states (a b c d and - = blank) can have current state of lattice such as a - b c d c a or pictorially with coloured squares instead of a b c d Then neighbours of each cell are (typically) one on each side, or 2 on each side, or......

EASy Summer 2006Non Symbolic AI Lecture 1325 DDLabDDLab That coloured spacetime picture was taken from Andy Wuensche's page DDLab is Discrete Dynamics Lab Wuensche's work allows one to run CAs backwards, to see what previous state(s) of the world could (according to the rules) have preceded the present state.